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Hilbert Space in Quantum Mechanics

  1. Jun 3, 2013 #1
    in quantum mechanics we have something called hilbert space. What does the dimensions of this space represent for that system?
    also is ψ(x) same as |ψ> in the dirac notation?
     
    Last edited: Jun 3, 2013
  2. jcsd
  3. Jun 3, 2013 #2

    bhobba

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    The dimension gives the number of possible outcomes of an observation. If infinite dimensional it's countably infinite but the possible outcomes can either be countably infinite or a continuum.

    ψ(x) is the representation of |ψ> in terms of the eigenvectors of the position operator.

    If that doesn't make sense you really need to learn about vector spaces and the Dirac notation:
    http://en.wikipedia.org/wiki/Bra–ket_notation

    Thanks
    Bill
     
    Last edited: Jun 3, 2013
  4. Jun 10, 2013 #3
    The dimension gives the number of possible behavior of particle, with regards to it directions.
    ψ(x) is the representation of scalar and as well |ψ> in terms of the eigenvectors of the position operator. but in the Dirac notation their are both Spinor in terms of matrices . one ψ(x)_[1] consists of two up spin and the other ψ(x)_[2]consists of two spin downward..
     
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